%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET078-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:59 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.42s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 8 unt; 0 def)
% Number of atoms : 10 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f133,negated_conjecture,
~ member(singleton(y),unordered_pair(x,singleton(y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_singletons_are_sets_1) ).
fof(f135,plain,
~ member(unordered_pair(y,y),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f133,f12,f12]) ).
fof(f155,plain,
~ member(unordered_pair(y,y),unordered_pair(unordered_pair(y,y),x)),
inference(superposition,[],[f135,f120]) ).
fof(f163,plain,
~ member(unordered_pair(y,y),universal_class),
inference(resolution,[],[f9,f155]) ).
fof(f166,plain,
$false,
inference(forward_subsumption_resolution,[],[f163,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET078-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 00:35:12 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.63/1.42 % (1081214)Input is clausal, will run a generic CNF schedule.
% 3.63/1.42 % (1081219)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3687241160:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.63/1.42 % (1081225)dis-21_1_sil=8000:lcm=predicate:random_seed=1003948040:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.63/1.42 % (1081220)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=666222129:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.63/1.42 % (1081224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2136029841:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.63/1.42 % (1081221)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=271354310:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.63/1.42 % (1081222)lrs+10_1_sil=8000:sp=occurrence:random_seed=313688522:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.63/1.42 % (1081223)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1951755010:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.63/1.42 % (1081222)Also succeeded, but the first one will report.
% 3.63/1.42 % (1081223)First to succeed.
% 3.63/1.42 % (1081223)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1081214"
% 3.63/1.42 % (1081225)Also succeeded, but the first one will report.
% 3.63/1.42 % (1081224)Also succeeded, but the first one will report.
% 3.63/1.42 % (1081223)Refutation found. Thanks to Tanya!
% 3.63/1.42 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.42 % (1081223)------------------------------
% 3.63/1.42 % (1081223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.42 % (1081223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.42 % (1081223)CaDiCaL version: 2.1.3
% 3.63/1.42 % (1081223)Termination reason: Refutation
% 3.63/1.42 % (1081223)Time elapsed: 0.003 s
% 3.63/1.42 % (1081223)Peak memory usage: 88 MB
% 3.63/1.42 % (1081223)Instructions burned: 2 (million)
% 3.63/1.42 % (1081223)------------------------------
% 3.63/1.42 % (1081223)------------------------------
% 3.63/1.42 % (1081214)Success in time 0.438 s
% 3.63/1.42 % Vampire exiting
%------------------------------------------------------------------------------